Mathematik, Informatik und Statistik - Open Access LMU - Teil 01/03

Ludwig-Maximilians-Universität München
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Die Universitätsbibliothek (UB) verfügt über ein umfangreiches Archiv an elektronischen Medien, das von Volltextsammlungen über Zeitungsarchive, Wörterbücher und Enzyklopädien bis hin zu ausführlichen Bibliographien und mehr als 1000 Datenbanken reicht. Auf iTunes U stellt die UB unter anderem eine Auswahl an elektronischen Publikationen der Wissenschaftlerinnen und Wissenschaftler an der LMU bereit. (Dies ist der 1. von 3 Teilen der Sammlung 'Mathematik, Informatik und Statistik - Open Access LMU'.)

  1. 01/01/2002

    A Selection Model for Bivariate Normal Data, with a Flexible Nonparametric Missing Model and a Focus on Variance Estimates

    Nonignorable nonresponse is a common problem in bivariate or multivariate data. Here a selection model for bivariate normal distributed data (Y1 ; Y2) is proposed. The missingness of Y2 is supposed to depend on its own values. The model for missingness describes the probability of nonresponse in dependency of Y2 itself and it is chosen nonparametrically to allow exible patterns. We try to get a reasonable estimate for the expectation and especially for the variance of Y2 . Estimation is done by data augmentation and computation by common sampling methods.

  2. 01/01/2002

    A Smooth Test in Proportional Hazard Survival Models using Local Partial Likelihood Fitting

    Proportional hazard models for survival data, even though popular and numerically handy, suffer from the restrictive assumption that covariate effects are constant over survival time. A number of tests have been proposed to check this assumption. This paper contributes to this area by employing local estimates allowing to fit hazard models with covariate effects smoothly varying with time. A formal test is derived to test the model with proportional hazards against the smooth general model as alternative. The test proves to possess omnibus power. Comparative simulations and two data examples accompany the presentation. Extensions are provided to multiple covariate settings, where the focus of interest is to decide which of the covariate effects vary with time.

  3. 01/01/2002

    A comparison of asymptotic covariance matrices of three consistent estimators in the Poisson regression model with measurement errors

    We consider a Poisson model, where the mean depends on certain covariates in a log-linear way with unknown regression parameters. Some or all of the covariates are measured with errors. The covariates as well as the measurement errors are both jointly normally distributed, and the error covariance matrix is supposed to be known. Three consistent estimators of the parameters - the corrected score, a structural, and the quasi-score estimators - are compared to each other with regard to their relative (asymptotic) efficiencies. The paper extends an earlier result for a scalar covariate.

  4. 01/01/2002

    An exact corrected log-likelihood function for Cox's proportional hazards model under measurement error and some extensions

    This paper studies Cox`s proportional hazards model under covariate measurement error. Nakamura`s (1990) methodology of corrected log-likelihood will be applied to the so called Breslow likelihood, which is, in the absence of measurement error, equivalent to partial likelihood. For a general error model with possibly heteroscedastic and non-normal additive measurement error, corrected estimators of the regression parameter as well as of the baseline hazard rate are obtained. The estimators proposed by Nakamura (1992), Kong, Huang and Li (1998) and Kong and Gu (1999) are reestablished in the special cases considered there. This sheds new light on these estimators and justifies them as exact corrected score estimators. Finally, the method will be extended to some variants of the Cox model.

  5. 01/01/2002

    Application of Survival Analysis Methods to Long Term Care Insurance

    With the introduction of compulsory long term care (LTC) insurance in Germany in 1995, a large claims portfolio with a significant proportion of censored observations became available. In first part of this paper we present an analysis of part of this portfolio using the Cox proportional hazard model (Cox, 1972) to estimate transition intensities. It is shown that this approach allows the inclusion of censored observations as well as the inclusion of time dependent risk factors such as time spent in LTC. This is in contrast to the more commonly used Poisson regression with graduation approach (see for example Renshaw and Haberman 1995) where censored observations and time dependent risk factors are ignored. In the second part we show how these estimated transition intensities can be used in a multiple state Markov process (see Haberman and Pitacco, 1999) to calculate premiums for LTC insurance plans.

  6. 01/01/2002

    Comparing Different Estimators in a Nonlinear Measurement Error Model

    A nonlinear structural errors-in-variables model is investigated, where the response variable has a density belonging to an exponential family and the error-prone covariate follows a Gaussian distribution. Assuming the error variance to be known, we consider two consistent estimators in addition to the naive estimator. We compare their relative efficiencies by means of their asymptotic covariance matrices for small error variances. The structural quasi score (SQS) estimator is based on a quasi score function, which is constructed from a conditional mean-variance model. Consistency and asymptotic normality of this estimator is proved. The corrected score (CS) estimator is based on an error-corrected likelihood score function. For small error variances the SQS and CS estimators are approximately equally efficient. The polynomial model and the Poisson regression model are explored in greater detail.

  7. 01/01/2002

    Generalized basic probability assignments

    Dempster-Shafer theory allows to construct belief functions from (precise) basic probability assignments. The present paper extends this idea substantially. By considering SETS of basic probability assignments, an appealing constructive approach to general interval probability (general imprecise probabilities) is achieved, which allows for a very flexible modelling of uncertain knowledge.

  8. 01/01/2002

    Geo-additive models of Childhood Undernutrition in three Sub-Saharan African Countries

    We investigate the geographical and socioeconomic determinants of childhood undernutrition in Malawi, Tanzania and Zambia, three neighboring countries in Southern Africa using the 1992 Demographic and Health Surveys. We estimate models of undernutrition jointly for the three countries to explore regional patterns of undernutrition that transcend boundaries, while allowing for country-specific interactions. We use semiparametric models to flexibly model the effects of selected so-cioeconomic covariates and spatial effects. Our spatial analysis is based on a flexible geo-additive model using the district as the geographic unit of anal-ysis, which allows to separate smooth structured spatial effects from random effect. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques. While the socioeconomic determinants generally confirm what is known in the literature, we find distinct residual spatial patterns that are not explained by the socioeconomic determinants. In particular, there appears to be a belt run-ning from Southern Tanzania to Northeastern Zambia which exhibits much worse undernutrition, even after controlling for socioeconomic effects. These effects do transcend borders between the countries, but to a varying degree. These findings have important implications for targeting policy as well as the search for left-out variables that might account for these residual spatial patterns.

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Die Universitätsbibliothek (UB) verfügt über ein umfangreiches Archiv an elektronischen Medien, das von Volltextsammlungen über Zeitungsarchive, Wörterbücher und Enzyklopädien bis hin zu ausführlichen Bibliographien und mehr als 1000 Datenbanken reicht. Auf iTunes U stellt die UB unter anderem eine Auswahl an elektronischen Publikationen der Wissenschaftlerinnen und Wissenschaftler an der LMU bereit. (Dies ist der 1. von 3 Teilen der Sammlung 'Mathematik, Informatik und Statistik - Open Access LMU'.)

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